Function

Class Name

• RFunction

Location in Objects Pane

• Models > Function

Properties

Object Name

• Name of the object in Rt.
• Allowable characters include upper-case and lower-case letters, numbers, and underscore (“_”).
• The name is unique and case-sensitive.

Expression

• Indicates the expression of the limit state function, for example:

1.0 - x2/(1000.0*x3) - (x1/(200.0*x3))^2

• The following functions can be used in the expression of the function:

Name	No. of Arguments	Explanation
sin	1	sine function
cos	1	cosine function
tan	1	tangent function
asin	1	arcus sine function
acos	1	arcus cosine function
atan	1	arcus tangent function
sinh	1	hyperbolic sine function
cosh	1	hyperbolic cosine
tanh	1	hyperbolic tangent function
asinh	1	hyperbolic arcus sine function
acosh	1	hyperbolic arcus cosine function
atanh	1	hyperbolic arcus tangent function
log2	1	logarithm to the base 2
log10	1	logarithm to the base 10
log	1	logarithm to the base 10
ln	1	logarithm to base e (2.71828...)
exp	1	e raised to the power of x
sqrt	1	square root of a value
sign	1	sign function -1 if x<0; 1 if x>0
rint	1	round to nearest integer
abs	1	absolute value
if	3	if ... then ... else ...
min	var.	min of all arguments
max	var.	max of all arguments
sum	var.	sum of all arguments
avg	var.	mean value of all arguments

• The following operators can be used in the expression of the function:

Operator	Meaning	Priority
=	assignment	-1
and	logical and	1
or	logical or	1
xor	logical xor	1
<=	less or equal	2
>=	greater or equal	2
!=	not equal	2
==	equal	2
>	greater than	2
<	less than	2
+	addition	3
-	subtraction	3
*	multiplication	4
/	division	4
^	raise x to the power of y	5

Gradient Analysis Type

• Indicates the methods to compute the gradient of the limit-state function, including finite difference method and direct difference method.
• For more information, see Zhang-Der Kiureghian (1993) and Kleiber (1997)

Perturbation Factor

• The forward finite difference estimate of gradient vector for each variable is equal to its standard deviation divided by Perturbation Factor which is typically set equal to 1000.

Efficient Perturbation

• Efficient perturbation restricts Rtx to use perturbed values only for the models that are affected by variables' changes to recalculate function value. Two options are available: if the option “True” is set, program will run models affected by perturbation recognized by Rt, and in case the “False” option is set, the program will run all models for each perturbation.

Read-only Properties

Function Value

• The current value of function as the results of calculations

Output

• Limit-state function

Right-click Menu

Remove

• Removes the object.

References

• Zhang, Y., & Der Kiureghian, A. (1993). Dynamic response sensitivity of inelastic structures. Computer Methods in Applied Mechanics and Engineering, 108(1), 23–36
• Kleiber, M. (1997). Parameter sensitivity, J. Willey & Sons Ltd., Chichester